Correct question is:

Find the value of x if

tan^-1 (x + 2)+ tan^-1 (x - 2) = tan^-1 (8/79);  x > 0

Given, tan^-1 (x + 2)+ tan^-1 (x - 2) = tan^-1 (8/79)

=> tan^-1 [{(x + 2) + (x - 2)}/{1 - (x + 2) * (x - 2)}] = tan^-1 (8/79)

=> tan^-1 [2x/{1 - (x² - 4)} = tan^-1 (8/79)

=> tan^-1 [2x/{1 - x² + 4)} = tan^-1 (8/79)

=> tan^-1 [2x/{5 - x² )} = tan^-1 (8/79)

=> 2x/(5 - x² ) = 8/79

=> x/(5 - x² ) = 4/79

=> 79x = 20 - 4x²

=> 4x² + 79x - 20  = 0

=> (4x - 1)*(x + 20) = 0

=> x = 1/4, -20

Since x > 0

So, x = 1/4

Hence, the value of x is 1/4